Pythagoras was among the most celebrated philosophers of the Antique period. He supposedly was “the first to bring to the Greeks philosophy in general” and was the first to use the term ‘philosophy’ and to call himself a ‘philosopher.” His teaching focused on mathematics and rational inquiry, yet was thoroughly esoteric.

He is said to have traveled very broadly and to have incorporated teaching from everywhere he went. It is said that he met with and learned from Thales, as well as Anaximander. He is also thought to have studied geometry with the Egyptians and to have gained knowledge of ethics at Delphi. His esoteric teaching would have been particularly influenced by learning of the Orphic mysteries from Aglaophamus and to his initiation into the mysteries of Egyptian religion.

There are many myths surrounding Pythagoras’ life. One myth was that he had descended into Hades. Another was that he remembered his earlier lives, indeed that his soul had wandered and could remember “all the plants and animals it had been in and everything that his soul had experienced in Hades and that other souls there endure.” There are myths of him being a miracle worker. Some even worshiped him as a god.

The school that he founded, which is said to have lasted ten generations, was a sect devoted to theoretical learning, moral training, but also a strong indoctrination. There were levels to the initiation. Learners who joined the school would initially be silent for five years. After being tested they would then belong to the “household.” In the Pythagorean school, students were prohibited from eating animals, except for those that were allowed for sacrifices. Those were the animals into which the human soul does not migrate. Pythagoreans were “to abstain from beans as though from human flesh…and from almost all creatures of the sea.”

In a story surely apocryphal given its poetic (in)justice, Pythagoras is said to have died after the house where he was visiting Milo the Wrestler was set afire. He fled, but the jealous people who set the house ablaze caught up with him at a bean field when he refused to cross it. They there slit his throat. We might assume the tale is meant to sarcastically point out the absurdity of not eating beans, which were not consumed because they looked “like testicles or the gates of Hades.”

Despite the strangeness of the apocryphal stories surrounding Pythagoras and his school, we see in him great learning. He viewed the reality as numerical. He formalized the Pythagorean theorem, named after him. He and his students also came to understand the ratio character of musical scales. Along with Parmenides and the Eleatics he represents an epistemological orientation that is important in the development of Western thought — the focus of his thought being not primarily on sense experience but on concepts and logic. His focus, in particular, was on mathematical knowledge. With this focus, along with Parmenides, he was a was influence on Plato.

Side by side with great learning, however, Pythagoras and his students also displayed great dogmatism. Hippasus, who is said to have revealed how to draw the dodecahedron (and is thought by some to have developed the idea irrational numbers and thereby undermined the Pythagorean view of the rationality of the universe), was killed by the Pythagoreans, cast to sea.

One of the earliest disputes of the Greek naturalists and Eleatics concerned the question of the one and the many — that is was the substratum of the natural world or reality itself one substance or many? Parmenides is clearly a monist, who thought that all change and difference in the world was essentially illusory. Yet Thales, Anaximander, and Anaximenes were also monists. While they accept that there are many diverse entities in the world, they argue that the substrate underlying them or the primal stuff from which they emerge is singular. For Thales, they are all made of water. For Anaximander, they all come from the original unity of the unbound. For Anaximenes, they all stem from an original chaos but have aether as their basic element. Some of those who most clearly argue that the basic components of the world are not singular but multiple have not been mentioned.

Empedocles, who many early Greeks viewed as responsible for the developed teaching of the elements, is thought a pluralist. There is not one substance underlying the diverse things in the world; rather, there are a few key ones. The change we view in the world occurs over and above a “mingling and separating” of things that are themselves unchanging, primary oppositions: Wet, dry, cold and warm are eternal qualities that comprise all things, but that are propelled in their motion by two other eternal powers that also pull in opposition to one another, love and strife. The various things in the world around us do undergo change and transition as these eternal elements and forces ascend and recede from the foreground. Yet these basic qualities themselves are eternal. Basic reality, ultimate reality is not singular but plural. Empedocles is not a monist but a pluralist.

Another great “Presocratic” pluralist is Democritus, who was born just after Socrates, around 460 BCE — a reminder of the trouble with the temporal designation of “Presocratics.” The atomists maintain that the primary components from which all things in the world are comprised are atoms. From eternity, they have existed, with slightly different shapes and sizes. All things combine from a mixture of atoms and void. But the reality is expressed not by qualities of things. “By convention sweet and by convention bitter, by convention hot, by convention cold, by convention color: in reality atoms and void.” Qualities that we experience only have an apparent reality. Some of the Ancients viewed Democritus as a skeptic, but Sextus, an early commentator on Greek natural philosophy, has contributed to a common view that makes greater sense in view of his various truth claims:

In the Rules[Democritus] says that there are two kinds of knowing, one through the senses and the other through the understanding. The one through the understanding he calls genuine, witnessing to its trustworthiness in deciding truth; the one through the senses he names bastard, denying it steadfastness in the discernment of what is true. He says in these words, “There are two forms of knowing, one genuine and the other bastard. To the bastard belong all these: sight, hearing, smell, taste, touch. The other, the genuine, has been separated from this.” Then preferring the genuine to the bastard, he continues, saying, “Whenever the bastard is no longer able to see more finely nor hear nor smell nor taste nor perceive by touch, but something finer…

Over the course of time, Democritus sees the atoms combining into different formations, which for their part then again dissemble. In fact, the atomists propose an idea that various other Presocratics also shared — that over the course of time the cosmos emerges, then collapses only to later re-emerge.

Hans Georg Gadamer, an important 20th century Germany hermeneutical philosopher, emphasizes … the importance of Parmenides and the Eleatics for Plato’s later theory of the forms. Like Plato … Parmenides, as well as Zeno and other Eleatics, dismisses sense experience as a source of truth. For these thinkers, it is the analysis of concepts that lead to a truth that one must affirm regardless of how out of sync it is with our common understanding of the world.

In Parmenides case, the great rational revelation concerned the constancy and unchangeability of Being. “What is is,” he wrote, “and what is not is not.” If something were to come into being, then it would now be nothing. But nothing cannot exist. Similarly, if something now existed it could not later no longer exist. If so, where there is now something there would later be nothing. But nothing cannot exist.

For Parmenides, the eyes and ears lead us astray. As he notes: “Seeing, they saw in vain; Listening, they failed to hear.” In his view, following the logic of the argument, we should recognize that Being is unitary and unchanging. Our ordinary, temporal understanding, it follows, must be illusory. Being must, by definition, be eternal without beginning and without end.

Other Eleatics, like Zeno, followed in Parmenides’ footsteps. Zeno developed a series of logical paradoxes to underline the Parmenidean view that change, as perceived by sense experience, is illusory. Zeno’s arrow paradox plays on a concept of time. If an arrow is shot toward a target, at any given instance in time it would find itself at rest at some place on the trajectory. Since at every instant the arrow is at rest, it could never move from the arrow to the target. Logic, Zeno argues, disproves that movement is possible. We should thus not trust our senses.

His racecourse paradox reaches a similar conclusion. Imagine Homer running toward a target. To get there, he would first have to get halfway there and to get halfway, he would first have to get to the half-way point of that half-way, ad infinitum. Between each space, however, there would be an infinite number of points to cross from one to another, since each half can again, mathematically be divided in half, ad infinitum. It is impossible to cross an infinitude, so the motion can never occur. The race could never start.

Though these paradoxes clearly have something wrong with them, they are mind-bending What are the problems with taking logic and applying it to realities of space and time in this way? Aristotle criticizes Zeno, as well as Plato. Plato, for his part, follows the lead of the Eleatics. He thinks we should follow reason even if it conflicts with sense experience. He like the Eleatics is thus known as a rationalist.

More than anything, Heraclitus is known as the philosopher of flux. As is famously attributed to him: “One cannot step in the same river twice” (D 91). Or as he similarly notes elsewhere: “As they step into the same rivers, other and still other waters flow upon them.”

Though it is important to understand Heraclitus as a great speculative philosopher who exceeds the Ionians in complexity, it is also important to see that he sets out similarly to the Ionians — so it is not without reason that Plato classifies all these early thinkers together as “Heracletians.” As Heraclitus says, indicating his similarity to the Ionians regarding the source of knowledge: “Whatever comes from sight, hearing, learning from experience: this I prefer” (D 55). Yet, seeing and hearing are not enough. To this, as the Ionians also appear to have clearly recognized, one must add understanding. “Eyes and ears are bad witnesses for those who have barbarian souls” (D 107).

While reasoning is as important as experience, it is not something that Heraclitus unhinges from experience. Heraclitus does not engage in the same abstract thought as Parmenides, speculating on the basis of an apriori logic. For him, the world around us, where one is born grows old dies, where all things change, serves as the basis of speculation. And that speculation should lead us to see the shifts and changes occur in accord with a law-like substratum. Here he posits a teaching of both logos (of word or mind or principle) and the elements. In this “All things are one.” Yet that unity contains diversity with the process: “Fire lives the death of earth and air lives the death of fire; water lives the death of air, earth that of water.” Individual objects in the world emerge and fade away out of a relationship of the transformation of elements through time.

Though Heraclitus will refer to the logos as divine, he does not speak of it as an external force acting upon a separate material. The process of the material change of the basic elements (with fire as the most basic) is not imposed by external deities, but is the order of the cosmos itself: “The ordering, the same for all, no god nor man has made, but it ever was and is and will be: fire everliving, kindled in measures and in measures going out.” Fire, the fundamental element, which also best symbolizes the transformation of the cosmos, transforms into the other elements in a process of continual change, where difference is fundamental, but difference persists in a process of unity.

One of Heraclitus’ fundamental themes is that this change in cosmos occurs through the balancing of oppositions. As he notes: “What is in opposition is in agreement, and the most beautiful harmony comes out of things in conflict (and all happens according to strife.)” Or more poetically, dismissing those who strive to see all conflict disappear: “They do not comprehend how being at variance it agrees with itself: it is a harmony turning back upon itself like a bow and a lyre.” This conflict between opposites is fundamental to the unfolding of the logos in the cosmos. In contrast to Hesiod who sees this conflict as a curse, Heraclitus posits that strife is not only “the father of all;” “strife is [also] justice.”

Beyond merely seeing how apparent conflicts complement one another, the “divine,” objective view of the cosmos that he stresses strives to rise above the common human-centric vision of reality. As he notes: “Sea is the most pure and most polluted water. For fish it is drinkable and life-preserving; for people it is undrinkable and deadly.”

Part of Heraclitus project is to reconceive of the divinity. It is now the cosmos as a whole or the logos that permeates it. Specific gods are part of this, but demythologized and viewed as functions of a law-like determinate universe. He notes the tension of his time, as myths are being secularized: “The one and only wise thing is and is not willing to be called by the name of Zeus.”

While this approach to reconceiving the gods is not unique to Heraclitus, he is more radical than most in that he not only rejects the traditional views of the gods, but also the rites and ceremonies honoring them, which he sees as having a corrosive effect on human beings. As he notes of ancient rites to Dionysos: “If it were not in honor of Dionysos that they organize a procession and sing the phallic hymn, what they do would be most shameless: but Hades and Dionysos are one and the same, in whose honor people rave and celebrate the Bacchic revelry.”

It is not the honoring of the gods that determine one’s fate and well-being. Rather: “Mans character is his fate.” The responsibility for what one becomes lies with oneself. Against this backdrop, Heraclitus notes: “the people should fight on behalf of the law as (they would) for (their) city wall.”

Heraclitus does re-conceive of the divine and of nature. One dovetails into the other. He bases his speculative reasoning on the senses but thinks it takes one beyond them. At least the knowledge that we have of him surpasses that of the Ionians by explicitly taking up not only issues of natural philosophy and metaphysics but also issues of ethics and teaching of the soul. In this, he among the Presocratics is the first to approach the systemic character of the later thought of Plato and Aristotle.

The very first of the Greek thinkers — the Ionians — lived in Asia Minor, in present-day Turkey. They were speculative natural philosophers. Thales, who Aristotle considered the first philosopher, speculated that the various distinct objects of the world all had the same substratum. Underneath the appearance of division in the world, there was a basic material unity: All things were comprised of water. While this is a scientific statement about what comprises reality, it is also a metaphysical statement. It is maintaining a basic unity among diversity.

We do not know precisely why Thales speculated that the common substance of all things was water. Aristotle speculated that it was because water is necessary for all living things. Water could also take the forms of solid (as ice), gas (as steam) and liquid (as water). In any case, what is remarkable about Thales’ view is not really the specific answer that he provides to the question. It is more the approach he initiates to address questions. He is not like the religious poet who comes bearing a message from the gods — his thoughts are not gifts of Hermes. Rather, he is speculating posting natural causes and using natural reason.

What Thales begins, various Ionian philosophers after him continue. Anaximander goes further than Thales, positing views about the origin of the diverse things in the world from a primordial unity. In the beginning was the Apeiron, the boundless or unlimited, a nondifferentiated unity. Out of it, the many things of the world emerge. Decisive here as a break in the explanatory model of the Greek religious-mythical thinkers, the emergence of the world does not occur because of the action of the gods. Neither Zeus nor Prometheus is involved. Rather, it is fundamentally the interaction of two factors — hot and cold — that are at work as the world emerges out of the unlimited. Animals are born from moisture heated by the sun. Humans originate from similar processes — natural and lawlike, even if not so clearly articulated as we might like.

Anaximenes continues reflections on these same issues. He proposes views contrasting with those of both Thales and Anaximander. Not water, he thinks, is the substratum, but air, aether. Following Anaximander, he appears to wonder that if all were comprised of water, how we would account for fire. Yet, in contrast to Anaximander, he posits a clearer mechanism through which the many arise from the original unity. The starting point for the development of the world was not the unbound but was chaos. Out if it, from a primordial breath, the many arise.

One of the main characteristics that we see in these earliest Ionian thinkers is that they do not take the authority of their tradition as a starting point for their reasoning. While they are undoubtedly influenced by that tradition, they set out to reason on the basis of what they experience …